If this is an FRS type radio, many models come with tone encoding for speaker muting. This means that when the transmit unit sends, it puts a very low frequency tone on the audio which the receiving unit picks out. There are several tone frequencies and if you match up the transmit one and recieve one by programming the radios correctly, then the reciever speaker unmutes only when it hears that tone.
I mention this because one of the biggest problems you will have with any walkie talkie is that it will receive interference from other people's transmissions and you need some way of making sure that your switch control only listens to your transmission, not the others. This tone function is one way to help insure that.
However, in addition, it might be wise to send a simple tone over the radio and then use a tone decoder on the receiver. It would be easy to interface the encoder to the transmit unit microphone and the decoder to the receive unit speaker. The output of the tone decoder would be your switch driver. The old standard tone encoders and decoders are the LM566 and LM567 but there may be newer and better chips now. Perhaps try Maxim.